Finite Group Databasebeta

← C2×#16840092 #21455696

Subgroups — C2×#16840092 #21455696

Order 7808.

460 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519756C211yesmaximal, characteristic
2#16840092C218yesmaximal, direct product factor
3C2×#14519708C212yesmaximal, complemented
4C2×#14519700C212yesmaximal, complemented
5C2×C22⋊#92418C211yesmaximal, characteristic
6C22×C4⋊C4×C61C211yesmaximal, characteristic
7C22×Dic122C2211yescharacteristic
8C22×#92418C2212yes—
9#14519756—22no—
10#14519756C2214yes—
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196—21no—
13C2×C22⋊Dic61—21no—
14#14519708C2218yescomplemented
15#14519700C2218yescomplemented
16C22⋊#92418C2214yes—
17C23×C4×C61—21no—
18C23×C4×C61C2211yescharacteristic
19C2×C4⋊C4×C61—21no—
20C2×C4⋊C4×C61—22no—
21C2×C4⋊C4×C61C2212yes—
22C2×C4⋊C4×C61C2214yes—
23C24×C61D411yescharacteristic
24C22×C4×C61—24no—
25C22×C4×C61—24no—
26C22×C4×C61—22no—
27C22×C4×C61—44no—
28C22×C4×C61D411yescharacteristic
29C22×C4×C61D412yes—
30C22×C4×C61C2312yes—
31C22×C4×C61C2311yescharacteristic
32C22×Dic61—21no—
33C22×Dic61—21no—
34C2×Dic122—24no—
35C2×Dic122—21no—
36C2×Dic122C2312yes—
37C4⋊C4×C61—24no—
38C4⋊C4×C61—22no—
39C4⋊C4×C61C2314yes—
40C22⋊Dic61—24no—
41C4⋊Dic61—21no—
42C4⋊Dic61C2312yes—
43#11758196—24no—
44C2×#92418—24no—
45C2×#92418C2314yes—
46C23×C61—22no—
47C23×C61—22no—
48C23×C61SD1614yes—
49C23×C61C2×D412yes—
50C23×C61C2×D411yescharacteristic
51C2×C4×C61—22no—
52C2×C4×C61—24no—
53C2×C4×C61—24no—
54C2×C4×C61—24no—
55C2×C4×C61—48no—
56C2×C4×C61—44no—
57C2×C4×C61C2×D412yes—
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61#4114yes—
60C2×C4×C61C2411yescharacteristic
61C2×Dic61—22no—
62C2×Dic61—22no—
63C2×Dic61—42no—
64C2×Dic61—42no—
65Dic122—24no—
66Dic122—42no—
67#92418—24no—
68C22×C61—22no—
69C22×C61—22no—
70C22×C61—28no—
71C22×C61#12312yes—
72C22×C61C2×SD1614yes—
73C22×C61C2×SD1612yes—
74C22×C61#13712yes—
75C22×C61C22×D411yescharacteristic
76C4×C61—22no—
77C4×C61—44no—
78C4×C61#12312yes—
79C4×C61C2×#4112yes—
80Dic61—42no—
81Dic61—42no—
82C2×#483—611nomaximal, Sylow
83C2×C61—24no—
84C2×C61#48314yescomplemented
85C2×C61C2×#12311yescharacteristic
86C2×C61C22×SD1611yescharacteristic
87C2×C61C2×#13711yescharacteristic
88C2×C22⋊Q8—611no—
89C22×C4⋊C4D6111yescharacteristic
90#483—618no—
91C2×#106—612no—
92C2×#103—612no—
93C2×C22⋊C8—611no—
94C61C2×#48311yescharacteristic, complemented, Sylow
95C22×Q8—611no—
96C23×C4—21no—
97C23×C4C2×D6111yescharacteristic
98C22×C8—612no—
99C22⋊Q8—614no—
100C22⋊Q8—1222no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—611no—
104C2×C4⋊C4—1221no—
105C2×C4⋊C4C2×D6112yes—
106C2×C4⋊C4C2×D6114yes—
107C2×C22⋊C4—1221no—
108#106—618no—
109#103—618no—
110C22⋊C8—614no—
111C24C22⋊D6111yescharacteristic
112C2×Q8—612no—
113C2×Q8—1221no—
114C2×Q8—1224no—
115C22×C4—24no—
116C22×C4—24no—
117C22×C4—22no—
118C22×C4—44no—
119C22×C4—1221no—
120C22×C4—1221no—
121C22×C4C22⋊D6112yes—
122C22×C4C22⋊D6111yescharacteristic
123C22×C4C22×D6112yes—
124C22×C4C22×D6111yescharacteristic
125C2×C8—614no—
126C2×C8—1224no—
127C4⋊C4—24no—
128C4⋊C4—22no—
129C4⋊C4—612no—
130C4⋊C4—1221no—
131C4⋊C4—1224no—
132C4⋊C4C22×D6114yes—
133C22⋊C4—1224no—
134C23—22no—
135C23—22no—
136C23#1175820014yes—
137C23C2×C22⋊D6112yes—
138C23C2×C22⋊D6111yescharacteristic
139Q8—1224no—
140Q8—2442no—
141C2×C4—22no—
142C2×C4—24no—
143C2×C4—24no—
144C2×C4—24no—
145C2×C4—48no—
146C2×C4—44no—
147C2×C4—1222no—
148C2×C4—1222no—
149C2×C4—2442no—
150C2×C4—2442no—
151C2×C4#1175822214yes—
152C2×C4C2×C22⋊D6112yes—
153C2×C4C2×C22⋊D6111yescharacteristic
154C2×C4C23×D6111yescharacteristic
155C8—1224no—
156C22—22no—
157C22—22no—
158C22—28no—
159C22#1451976012yes—
160C22C2×#1175820014yes—
161C22C2×#1175820012yes—
162C22#1451980812yes—
163C22C22×C22⋊D6111yescharacteristic
164C4—22no—
165C4—44no—
166C4—2442no—
167C4—2442no—
168C4#1451976012yes—
169C4C2×#1175822212yes—
170C2—24no—
171C2#1684009214yesdirect product factor
172C2C2×#1451976011yescharacteristic
173C2C22×#1175820011yescharacteristic
174C2C2×#1451980811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC22×C4⋊C4×C61C2
socleC23×C61C2×D4
hypercenterC22×C4⋊C4D61
hypocenterC61C2×#483
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #16840092C2direct (N × H)
3. C2×#14519708C2semidirect
4. C2×#14519700C2semidirect
14. #14519708C22semidirect
15. #14519700C22semidirect
84. C2×C61#483semidirect
94. C61C2×#483semidirect
171. C2#16840092direct (N × H)